The trainer in my gym told me that from doing squats you'll
get a bigger butt. But that's something that I don't want, because
of my body type I already have a big butt. :) He advised doing
leg press exercises instead. Other things that would speak for
doing LP exercises were (as he told me) that you can shift your
feet (not during the exercise of course). By placing them wider
you'll be training the abductors more, it would be better for
the hipbone, because the LP would not put so much pressure on
the hipbone as the squat. If you've trained your back the day
before you can let the back rest. I am acquainted with both exercises
how to do them correctly. What would you suggest, so that my
glutes won't be getting bigger?

Like
any muscle, the glutes
can get bigger from weight training when adequate calories are
consumed. Any basic exercise that includes the glutes can increase
muscle mass, including leg presses, particularly if particular
dietary restrictions are not implemented. The effects you get
from your program can largely be affected by diet as well as
exercise. It is, however, possible to seemingly reshape your
glutes by simultaneously decreasing body fat and restoring muscle
mass; tightening this area and creating the illusion of a higher,
more shapely rear end.

If you are not prepared to implement certain dietary changes
to lower your body fat or if you are already quite lean, leg
presses with the feet wider and not high on the platform would
certainly be one strategy to de-emphasize the development of
the glutes. Keep in mind though, at some point you may want to
try other exercises other than leg press, if not for continued
progress, for variety's sake, so workouts do not become so
mind numbingly boring.

If you are on a split program, consider performing one compound
exercise for the glutes and quads (leg presses for example) plus
an additional isolated exercise for the quads (such as leg extensions).

If you choose to perform squats, it is also possible to slightly
vary your biomechanics, so more emphasis is placed on your quads
and less on your glutes. Examine your form for the relative torque
at the knee versus the hip. See Squat
Analysis. Also, make sure you are not bent over at the hip
at the top of the squat. Consider extending your hips slightly
sooner than your knees if this is the case. Also, realize a deep
squat or leg press with fuller range of motion will emphasize
the glutes. For this reason, consider half squats. As suggested,
a wider stance may also decrease the relative evolvement of the
glutes and quads by decreasing the torque forces on hip and knee
extension, a modification you can do with many compound movements
such a squats or leg presses. The wider stance will indeed place
more force on the adductors,
particularly the ischial fibers of the adductor magnus on both
movements.

Exercises such as the front squat emphasize the quads and
de-emphasize the glutes by decreasing the torque of the hip relative
to the knee. Your knees may be at risk if you alter your form
too much though (eg: allowing your heels to come off the floor
or platform, placing your feet too low on leg press, etc), particularly
if they are not given the opportunity to adapt adequately to
the greater torque forces. See Adaptation
Criteria. Keep in mind, your exercise intensity may be compromised
if you shift too much emphasis to the quads and away from your
glutes. Exercise intensity appears to be a key factor in increasing
the metabolism hours after anaerobic exercise.

An alternative solution is to perform higher reps (12-15 reps)
on your glute / quad exercise and in addition, and perhaps in
addition, perform HIIT two
to three days per week. This will allow you to achieve the fat
burning benefits of performing anaerobic exercise with the largest
muscles of the body while de-emphasizing the muscle building
effects of a moderate repetition range.

Your posture and underdeveloped hamstrings
may contribute to the illusion of a larger bum. Even a slight
lordosis
posture may accentuate an already large posterior.

Obviously, if you tend to carry some of your body fat in the
rear quarters, a reduction of body fat may reduce its proportion
somewhat, although the hips and glutes may appear to be one of
the last places fat seems to be reduced in women (see Spot
Reduction Myth). Take regular
circumference measurements and body
composition tests so you will be able to make immediate modifications
to your program, particularly your diet, dependent upon the changes
of fat, lean body weight, and girths. See dietary
development.

In summary, examine your exercise biomechanics and possibly
slightly alter your form. Only perform a single exercise involving
the glutes and change exercises periodically. If your posture
or muscular proportions can be improved, regularly perform some
of the corrective exercises for lordosis or an additional exercise
for the hamstrings, respectively as needed. Finally, monitor
your body composition and girths, modifying your program accordingly.